GRE · Practice Sheet 8

1. 1.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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2. 2.

   Quantitative Aptitude

   The sum of the ages of two people is 70 years, and one is 2 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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3. 3.

   Quantitative Aptitude

   What is 10% of 600?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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4. 4.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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5. 5.

   Quantitative Aptitude

   Find the HCF and LCM of 36 and 36.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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6. 6.

   Quantitative Aptitude

   What is 40% of 100?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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7. 7.

   Mathematics

   Find the distance between the points (-6, 4) and (2, 1).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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8. 8.

   Quantitative Aptitude

   The sum of the ages of two people is 34 years, and one is 10 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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9. 9.

   Mathematics

   Evaluate ∫ from 0 to 4 of 2x^2 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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10. 10.

    Quantitative Aptitude

    Find the average of these 6 numbers: 81, 72, 28, 28, 37, 88.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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11. 11.

    Quantitative Aptitude

    A can finish a job in 14 days and B in 4 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

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12. 12.

    Mathematics

    Find the sum of the first 10 terms of an AP with first term 17 and common difference 7.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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13. 13.

    Quantitative Aptitude

    An item is bought for $200 and sold for $220. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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14. 14.

    Quantitative Aptitude

    A can finish a job in 20 days and B in 5 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

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15. 15.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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16. 16.

    Quantitative Aptitude

    The sum of the ages of two people is 68 years, and one is 10 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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17. 17.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

    $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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18. 18.

    Quantitative Aptitude

    A invests $2,000 and B invests $5,000 for the same period. If the total profit is $22,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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19. 19.

    Mathematics

    Find the slope of the line through (-1, -7) and (-2, 0).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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20. 20.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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